Jacob's ladders, reverse iterations and new infinite set of $L_2$-orthogonal systems generated by the Riemann $\zf$-function

Abstract

It is proved in this paper that continuum set of $L_2$-orthogonal systems generated by the Riemann zeta-function on the critical line corresponds to every fixed $L_2$-orthogonal system on a fixed segment. This theorem serves as a resource for new set of integrals not accessible by the current methods in the theory of the Riemann zeta-function. \noindent Dedicated to the 100th anniversary of G.H. Hardy's fundamental theorem: the function $\zf$ has an infinite set of zeros, \cite{1}.